Spatial stability in linear thermoelasticity

Abstract

Uniqueness and spatial stability are investigated for smooth solutions to boundary value problems in non-classical linearised and linear thermoelasticity subject to certain conditions on material coefficients. Uniqueness is derived for standard boundary conditions on bounded regions using a generalisation of Kirchhoff’s method. Spatial stability is discussed for the semi-infinite prismatic cylinder in the absence of specified axial asymptotic behaviour. Alternative growth and decay estimates are established principally for the cross-sectional energy flux that is shown to satisfy a first order differential inequality. Uniqueness in the class of solutions with bounded energy follows as a corollary. Separate discussion is required for the linearised and linear theories. Although the general approach is similar for both theories, the argument must be considerably modified for the treatment of the linear theory.